Books

  • The Three-Dimensional Navier-Stokes Equations
    with J.C. Robinson & W. Sadowski
    Cambridge Studies in Advanced Mathematics. Cambridge University Press. (in production)
  • Recent progress in the theory of the Euler and Navier-Stokes Equations
    London Mathematical Society Lecture Notes Series (No. 430), Cambridge University Press.
    Eds J.C. Robinson, J. Rodrigo, W. Sadowski & A. Vidal-Lopez (2015).
  • Mathematical Aspects of Fluid Mechanics
    London Mathematical Society Lecture Note Series (No. 402), Cambridge University Press.
    Eds. J.C. Robinson, J. L. Rodrigo & W. Sadowski (2012).
  • Partial Differential Equations and Fluid Mechanics
    London Mathematical Society Lecture Note Series (No. 364), Cambridge University Press.
    Eds. J.C. Robinson & J.L. Rodrigo (2009)

Research Articles

(the pdfs may differ from the final published version)
  • (submitted) Local existence for the non-resistive MHD equations in nearly optimal Sobolev spaces (with C. Fefferman, D. McCormick, & J. Robinson)
  • (submitted) Lower bounds on blowing-up solutions of the 3D Navier–Stokes equations in $ \dot{H}^{3/2} $, $ \dot{H}^{3/2} $ and $\dot{B}^{5/2}_{2,1} $, ( with D. McCormick, E. Olson, J.C. Robinson, A. Vidal-Lopez & Y. Zhou)
  • Local existence for the non-resistive MHD equations in Besov spaces. Advances in Mathematics (2016) Vol 286, 1-31 (with J-Y Chemin, D. McCormick & J.C. Robinson)
  • Construction of analytic almost sharp fronts. Archive for Rational Mechanics and Applications (2015), Vol 218, 123-162 (with Charles Fefferman).
  • Higher order commutator estimates and local existence for the non-resistive MHD equations and related models. Journal of Functional Analysis (2014) Vol 267, 1035- 1056. (with C. Fefferman, D.S. McCormick, and J.C. Robinson)
  • Existence and uniqueness for a coupled elliptic parabolic model with applications to magnetic relaxation. Archives for Rational Mechanics and Analysis (2014), Vol 214, 503-523 (with James C. Robinson & David S. McCormick).
  • Generalised Gagliardo Nirenberg inequalities using weak Lebesgue spaces and BMO, accepted in the Milan Journal of Mathematics (2013), Vol 81, no. 2, 265-289, (with James C. Robinson & D. S. McCormick).
  • Almost Sharp Fronts for SQG: the limit equations, Comm. Math. Phys. 313, (2012), 131 153, (with Charles Fefferman)
  • The spine of an SQG almost sharp front, Nonlinearity 25 (2012), 329 342, (with Charles Fefferman & Kevin Luli)
  • Analytic Sharp Fronts for SQG, Comm. Math. Phys. 303 (2011), no. 1, 261 288 (with Charles Fefferman)
  • Almost Sharp Fronts for SQG: the limit equations, Comm. Math. Phys. 313, (2012), 131 153, (with Charles Fefferman)
  • The spine of an SQG almost sharp front, Nonlinearity 25 (2012), 329 342, (with Charles Fefferman & Kevin Luli)
  • Analytic Sharp Fronts for SQG, Comm. Math. Phys. 303 (2011), no. 1, 261 288 (with Charles Fefferman)
  • On a One-Dimensional Nonlocal Flux with Fractional Dissipation, SIAM J. Math. Anal. 43 (2011), 507 526 (with Dong Li)
  • Exploding solutions for a nonlocal quadratic evolution problem, Revista Matematica Iberoamericana 26 (2010), no. 1, 295 332( with Dong Li and Xiaoyi Zhang) pdf
  • Wellposedness and regularity of solutions of an aggregation equation, Revista Matematica Iberoamericana 26 (2010), no. 1, 261 294( with Dong Li) pdf
  • Refined blowup criteria and nonsymmetric blowup of an aggregation equation, Advances in Mathematics 220, 6, (2009), 1717 1738.( with Dong Li) pdf
  • Finite-time singularities of an aggregation equation in R^n with fractional dissipation, Comm. Math. Phys. 287 (2009), no. 2, 687 703 ( with Dong Li) pdf
  • Contour dynamics for the surface quasi-geostrophic equation, in Partial Differential Equations and Fluid Mechanics. London Mathematical Society Lecture Note Series (No. 364).
  • Blow up for the generalized surface quasi-geostrophic equation with supercritical dissipation, Comm. Math. Phys. 286 (2009), no. 1, 111 124( with Dong Li) pdf
  • Blow up of solutions for a 1D transport equation with nonlocal velocity and supercritical dissipation, Advances in Mathematics, 217, no. 6, 2563 2568 (2008. (with Dong Li) pdf
  • On the evolution of sharp fronts for the quasi-geostrophic equation. Comm. Pure Appl. Math. 58, no. 6, 821 866 (2005). pdf
  • Evidence of singularities for a family of contour dynamics equations. (with D. Cordoba, M. A. Fontelos and A. M. Mancho) PNAS Vol 102, n 17, 5949 5952, April 26 (2005). PNAS link pdf
  • The vortex patch problem for the Quasi-Geostrophic equation.
    PNAS Vol 101, n 9, 2484 2486, March 2 (2004). (PNAS link) pdf
  • Almost sharp fronts for the surface Quasi-Geostrophic equation. (with D. Cordoba and C. Fefferman)
    PNAS Vol 101, n 9, 2487 2491, March 2 (2004). PNAS link pdf

Other articles

  • Entrevista con John Nash. Gaceta de la Real Sociedad Matematica Española pdf
  • Las matematicas de los fluidos: torbellinos, gotas y olas, Gaceta de la Real Sociedad Matematica Española